Mathematical modeling of deformations of flexible threads under their dynamic loading in the zone of material plasticity

Abstract

The object of study is a vertical flexible thread rotating at some distance around a vertical axis with a lateral load. The calculation is made for the dynamic load condition in the form of centrifugal forces depending on the displacement of the thread from the initial position. The geometric and physical nonlinearity of the flexible threads is taken into account. The proposed method is based on the theory of mathematical modeling using differential and integral calculus of functions of one and several variables as well as on the theory of resistance of materials. A method of the nonlinear calculation of the stress-strain state of flexible threads, taking into account the real properties of materials is proposed. The text of the calculation in the computer program MatchCAD for calculations of the thread, its deformation and tension was theoretically described and developed. The calculation results corresponded to the results obtained by the finite element method (the discrepancy is about 1%). The implementation of the method makes it possible to study the operation of structures outside the conditions of elastic work of the material. The comparative results of modeling inertia loaded rotating threads with linear properties of changes in their strength properties and in the case of nonlinearity of their properties are presented.